Tech Talk: Chassis Set-Up

The behaviour of a kart chassis depends on the forces acting on it and through it to the tyres. Sideways and vertical forces on the tyres determine the movement of the kart and its capacity to follow the line steered by the driver. Of course, forces also come from the acceleration of the kart horizontally and by gravity vertically. Both these accelerations must be multiplied by the mass of the kart (which is directly proportional to the weight) to obtain the value of the forces that are applied to the centre of gravity (or barycentre) of the chassis.

Centre of gravity
The centre of gravity is the point inside (sometimes outside for particular shapes) the volume of any object that can be considered the point where all the mass of the object is concentrated. This means the vertical force of gravity can be considered to be concentrated at such a point. Any other force that depends on the mass of the object, for example centrifugal force, can also be considered concentrated at the centre of gravity.

A kart’s centre of gravity
A kart is mainly composed of the driver, the chassis with the fuel tank and the engine. The centre of gravity is the result of the weight of these main bodies. If a kart was a sphere or a cube, the centre of gravity would be placed exactly in the centre. For irregular shapes, calculating the position of the centre of gravity is more complex. However, it turns out that the centre of gravity for a kart chassis and engine plus the driver is more or less in the driver’s stomach. Therefore if we shift the position of the seat, the centre of gravity will also shift. The seat can be moved horizontally or vertically so as to modify the centre of gravity’s position and these two modifications will give different effects on chassis performance.

How the horizontal position of the centre of gravity acts on chassis set-up
The first law of dynamics is:
F = m a
where ‘F’ is the force, ‘m’ the mass of the object on which the force acts and ‘a’ the acceleration of the body. If we consider the vertical force of gravity acting on the chassis/driver/engine combination, ‘m’ is the total mass while ‘a’ is the acceleration due to gravity (often indicated by g). If the centre of gravity can be imagined as all the kart’s mass concentrated in a single point, we can also consider the mass and its consequent vertical force (weight) distributed on the four tyres. If the centre of gravity moves forward by shifting the seat forward, the weight distribution will of course also move forward and the downward force will increase on the front tyres and decrease at the rear. We will naturally have the opposite effect by shifting the centre of gravity rearwards. This will change the balance of grip between the front and the rear tyres and consequently give a variation in oversteer and understeer. If we consider the distance between the front and rear wheels as ‘a’ and the distance between the centre of gravity and the front and rear wheels respectively equal to ‘b’ and ‘c’ we get:
b + c = a
The total force being ‘F’, we will have:
F1 = F b/a
F2 = F c/a
where ‘F1’ is the force acting on the rear tyres and ‘F2’ is the force on the front tyres.

How the vertical position of the centre of gravity acts on chassis set-up
Another parameter affecting the action of weight on chassis set-up is the height of the centre of gravity. If we consider this value to be ‘h’, then the momentum ‘M’ that tends to rotate the chassis around its longitudinal axis (tip it) when cornering is:
M = Fc h
where ‘Fc’ is the centrifugal force. So the higher the centre of gravity, the greater the momentum ‘M’.
The force acting on the external tyres that tends to keep the chassis flat instead of tipping is:
Fe = M/l = Fc h/l
where ‘l’ is the distance between the external tyres and the longitudinal axis of the chassis. So the higher the centre of gravity the greater the downward forces acting on the external tyres. This gives more grip on the external tyres but less grip on the internal ones.
The final force on the external rear tyre is:
Fex rear = Fe + F2/2 And on the external front tyre:
Fex front = Fe + F1/2
On the internal rear tyre the resulting force is:
Fint rear = F2/2 – Fe
And on the internal front tyre the resulting force is:
Fint front = F1/2 – Fe
This means that the higher the centre of gravity the more the vertical forces are distributed on the external tyres and the less they are distributed on the internal tyres. Kart chassis as well as competition cars usually work better the lower the centre of gravity is, since the weight and the vertical forces on the four wheels are distributed in a more uniform way, while grip, for a number of reasons, is more constant. It is also true that extremely high grip on external tyres, by raising the centre of gravity, helps in wet track conditions since those tyres will have a very strong downward force acting on them, giving better contact with the track.
Next month we will go deeper into the effects of seat positioning and look at practical methods for moving it.